Abstract: Non-interactive cryptographic computing, Fully Homomorphic Encryption (FHE), provides a promising solution for private neural network training on encrypted data. One challenge of FHE-based private training is its large computational overhead, especially the multiple rounds of forward and backward execution on each encrypted data sample. Considering the existence of largely redundant data samples, pruning them will significantly speed up the training, as proven in plain non-FHE training. Executing the data pruning of encrypted data on the server side is not trivial since the knowledge calculation of data pruning needs complex and expensive executions on encrypted data. There is a lack of FHE-based data pruning protocol for efficient, private training. In this paper, we propose, \textit{HEPrune}, to construct a FHE data-pruning protocol and then design an FHE-friendly data-pruning algorithm under client-aided or non-client-aided settings, respectively. We also observed that data sample pruning may not always remove ciphertexts, leaving large empty slots and limiting the effects of data pruning. Thus, in HEPrune, we further propose ciphertext-wise pruning to reduce ciphertext computation numbers without hurting accuracy. Experimental results show that our work can achieve a $16\times$ speedup with only a $0.6\%$ accuracy drop over prior work. The code is publicly available at \href{https://github.com/UCF-Lou-Lab-PET/Private-Data-Prune}.